What causes this deformation when switching to FK mode?
After you created a walk cycle as described in an earlier post: How should an animated character be moved while repeating a walk cycle? 

If only takes a few keyframes where you move the legs and arms



Note that the movement has to be in place, no keyframes must be added to the root bone.

Create a curve (This example uses a bezier circle) and add a Follow Path constraint to the root bone.



In the NLA editor add your action holding the walk cycle and set the repeat value that it matches the length of the animation.